Summary: The VS Code C# extension is being embraced and extended: it is currently open source, and built on OmniSharp. The roadmap is to move Microsoft's development to build the C# extension around LSP instead of OmniSharp, which will let some of the (neat) Visual Studio features plug into VS Code -- but these features will not themselves be open sourced.
> We plan to create a new “LSP Tools Host” component [...] which integrates both open-source components, like Roslyn and Razor, with closed-source components, offering a wider array of tooling capabilities. Once the “LSP Tools Host” is complete, this will become the default experience for the C# for VS Code extension. Existing users will be able to choose between the open-source OmniSharp powered system that exists today, or the new “'LSP Tools Host” which will provide access to additional experiences. The “LSP Tools Host” will not be open-sourced, but we plan to communicate with the community along the way to help guide our future plans.
I don't really use .NET for personal projects, but issues like this that demonstrate Microsoft's apparent conflict of interest when it comes to supporting the runtime and languages ensure I probably won't be volunteering to learn it.
> We plan to create a new “LSP Tools Host” component [...] which integrates both open-source components, like Roslyn and Razor, with closed-source components, offering a wider array of tooling capabilities. Once the “LSP Tools Host” is complete, this will become the default experience for the C# for VS Code extension. Existing users will be able to choose between the open-source OmniSharp powered system that exists today, or the new “'LSP Tools Host” which will provide access to additional experiences. The “LSP Tools Host” will not be open-sourced, but we plan to communicate with the community along the way to help guide our future plans.